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What do Gollum, the new Olympic stadium that's being built in London and the quest for sustainable energy have in common? They all involve the work of engineers. Engineering provides some of the most exciting applications of maths there are, and they impact on all our lives every day. To highlight the importance and excitement of engineering, we are launching the Constructing our lives project, which will bring you articles and podcasts on engineering, directly from the engineers themselves.

"Mathematics is biology's next microscope, only better." That's what the scientist Joel E Cohen once said of the power of mathematics to revolutionise biology and the biomedical sciences. And he was right. Maths enables scientists to understand complex organisms and diseases, it's crucial in developing sophisticated medical technology and materials, and we can even use it to model our psyche and intelligence. In this sense maths has become a genuine research instrument for biomedical sciences. The insight it gives them are on a par with the revolutionising power of the microscope.

How do you judge the risks and benefits of new medical treatments, or of lifestyle choices? With a finite health care budget, how do you decide which treatments should be made freely available on the NHS? Historically, decisions like these have been made on the basis of doctors' individual experiences with how these treatments perform, but over recent decades the approach to answering these
questions has become increasingly rational.

Infectious diseases hardly ever disappear from the headlines — swine flu is only the last in a long list containing SARS, bird flu, HIV, and childhood diseases like mumps, measles and rubella. If it's not the disease itself that hits the news, then it's the vaccines with their potential side effects. It can be hard to tell the difference between scare mongering and responsible reporting,
because media coverage rarely provides a look behind the scenes. So how do scientists reach the conclusions they do?

One of the greatest advances in the biomedical sciences has been the unravelling of our genetic code. This new understanding sheds light on what makes organisms function and how they are related to each other, helps to combat diseases, and to convict criminals. But it also poses great mathematical challenges: the genetic revolution is an information explosion which can only be tamed using mathematical methods.